Compressive Direction Finding Based on Amplitude Comparison

Compressive Direction Finding Based on Amplitude Comparison Ruiming Yang, Yipeng Liu, Qun Wan and Wanlin Yang Department of Electronic Engineering University of Electronic Science and Technology of China Chengdu, China { shan99, liuyipeng, wanqun, wlyang}@uestc.edu.cn Abstract—This paper exploits recent developments in compressive sensing (CS) to efficiently perform the direction finding via amplitude comprarison. The new method is proposed based on unimodal characteristic of antenna pattern and sparse property of received data. Unlike the conventional methods based peak-searching and symmetric constraint, the sparse reconstruction algorithm requires less pulse and takes advantage of CS. Simulation results validate the performance of the proposed method is better than the conventional methods. Keywords - direction finding; amplitude comparison; beam scanning; sparse reconstruction; compressive sensing.

I.

INTRODUCTION

With the development of radar technology and the complication of target background, more and more information which is not range but also angle need be known to target in order to track and orientate accurately. In most modern radar systems, the target direction of arrival is estimated by the monopulse technique [1], which in principle can work with just a single pulse. Different from the direction-finding methods of monopulse radar, there is another method that works as follows: The beam of radar antenna scans to find the user; then the user responses; finally the radar measures the strength of the response signal, and finds the user’s location to the radar by the modulation information of the pattern. As the radar antenna pattern has obvious peak features, so the user position relative to the radar can be determined directly using the estimated peak location method. There are many ways to estimate the peak position. An efficient algorithm for estimating the peak position of a sampled function is the Hilbert Transform interpolation algorithm [2]. The algorithm is a computationally efficient algorithm for the peak detection and position estimation of a signal function. It is based on a signal interpolation technique which relies on the Hilbert Transform of the sampled signal. Besides, another method such as the multi-resolution method which is able to overcome the sampling period’s influence on the peak position estimation accuracy, Fourier transform time shift invariant Methods and Sinc function interpolation method [3] can estimate the peak location too. This paper re-examines the angle estimation problem and uses recent results in sparse approximation [4] and This work was supported in part by the National Natural Science Foundation of China under grant 60772146, the National High Technology Research and Development Program of China (863 Program) under grant 2008AA12Z306 and in part by Science Foundation of Ministry of Education of China under grant 109139.)

compressive sensing to provide a fundamentally different direction finding method. First we get a sparse representation of the received signal and then the user’s location to radar is obtained by the sparse solution. Comparing with the traditional unimodal characteristic and symmetry constraints based maximum (SCBM) methods, the proposed one requires fewer pulses, is with the ability of compressed sampling, and achieves a much smaller estimation error than the traditional search method. This paper is organized as follows. The Compressed sensing review is described in Section II. In section III we presented the measurements model. We introduce four direction finding methods in section IV: the traditional maximum method and symmetry constraints based maximum method, the match pursuit and basis pursuit methods which based on the compressive sensing. Section V presents simulation results that validate the formulation and demonstrate significant performance increase over traditional maximum methods. Conclusions are presented in section VI. II.

COMPRESSED SENSING REVIEW

Sparsity widely exists in wireless signals [5]. Considering a signal x can be expanded in an orthogonal complete dictionary, with the representation as 

x N 1  Ψ N  N b N 1 



when most elements of the vector b are zeros, the signal x is sparse. And when the number of nonzero elements of b is S (S